Department of Mathematics
Hanover, NH 03755
Dan Rockmore is John G. Kemeny Parents Professor of Mathematics and Professor of Computer Science at Dartmouth College, where he has taught since 1991. He received his A.B. in Mathematics from Princeton University in 1984 and his Ph.D. from Harvard University in 1989. In 1995 he was one of only 15 scientists to receive a five-year Presidential Faculty Fellowship from the White House for excellence in education and research. He has held visiting positions at the National Center for Atmospheric Research, the Santa Fe Institute (where he is also a member of the external faculty and Director of the Complex Systems Summer School) and the Institute for Advanced Study in Princeton. He has served as a member of the IDA/Darpa Defense Sciences Study Group and remains a consultant to IDA. He has authored and co-authored numerous scientific articles and three technical books mainly around the topic of the theory and application of efficient algorithms for data analysis. He has applied his work to climate modeling, image and signal processing and the design of robust communications schemes. He is a co-founder of the (NSF/Keck-funded) fMRI Data Center, a publicly accessible database of neuroimaging data. His research is supported by the NIH, NSF, and the AFOSR. Rockmore has also become a nationally recognized expositor of mathematics. His writings have appeared in newspapers and magazines and some of his mathematically inspired essays can be heard on Vermont Public Radio, His popular book "Stalking the Riemann Hypothesis" (Random House) was longlisted for the 2006 Aventis Prize . He is also a co-producer of the NSF-funded documentary, "The Math Life", distributed by Films for the Humanities and Sciences, “Mind in the Machine - the Discovery of Artificial Intelligence,” and his film on the new math of the life sciences, "Living Math", is slated for completion in the fall of 2007.
The Math Life
This talk is a presentation (and post-performance Q&A) of "The Math Life," by Wendy Conquest, Bob Drake, and Dan Rockmore, a 51-minute documentary full of good humor and lively animation that gives a window into the kinds of people and problems that are a part of modern mathematics and mathematical research. The takeaway message is that mathematics is a broad subject full of both mystery and fun and the people who do it come from a wide range of backgrounds and talents.
Stalking the Riemann Hypothesis
Ever since the time of Euclid, many of the greatest mathematicians have puzzled over the way in which the prime numbers fall among the natural numbers, seeking a law to describe their somewhat less than steady appearance. One hundred and fifty years ago, a German mathematician, Bernhard Riemann, in a short paper that was his only contribution to number theory, found a way to state such a law, but its precision depends upon one gently stated "hypothesis" embedded in this brief work. The now famous and infamous "Riemann Hypothesis", a simple statement about a particular kind of mathematical function has kept mathematicians busy ever since, leading to surprising connections between primes, card shuffling, chaos, and quantum mechanics. In this talk we'll survey the history of the problem, from its early beginnings to today and show why the hunt to settle the Riemann Hypothesis is one of the most important problems in mathematics today.
All too often we see mathematics and the arts as two sides of the science/humanities coin. In this talk we'll see a place in which the two come naturally together in exciting new research. For in today's world in which almost all aspects of life are brought to the common medium of the computer, it is now possible to quantify and extract the style of an artist via computation. Examples are gleaned from the literary, visual, and dance arts, and include applications to the problem of authentication. Taken together this work reveals just how stylish math can be.
These days the media is all aflutter with the tremendous advances being made in the life and social sciences, ranging from new understandings of the origins of life, to the workings of the cell, the body, and even the mind, and ranging from the individual to ecosystems. Often, hidden beneath the fanfare is the crucial role that mathematics plays in enabling these great achievements in biology, medicine, ecology, and sociology. This talk will survey some of these recent mathematical hits and, in doing so, give a glimpse at the new and exciting frontier of applied mathematics found in the life sciences.
The FFT - An Algorithm the Whole Family Can Use
The Fast Fourier Transform or "FFT" is one of the most ubiquitous algorithms in all of computational mathematics. In this talk we'll explore the FFT from its astronomical origins in the prediction of celestial orbits, to its modern instantiation as the primary tool of digital signal processing, and then move on to its generalizations as a basic scheme for data analysis in the presence of symmetry - i.e., group theory. We'll see how this more general framework has proved useful in a variety of areas including biology, robotics, and even quantum computing.
These days life seems to be all about networks: the “six degrees of separation” embodied in our network of friendships, the network of neurons that gives rise to consciousness, the interacting pieces of the financial markets, even the physical networks of power grids and the Internet. In this talk we’ll see the history of the development of the field and discuss some of the new mathematics that people are developing to study the different kinds of connectivity that are part and parcel of life!
Million Dollar Mathematics
The Clay Foundation has put million dollar bounties on seven intriguing and important mathematical problems. They touch on such things as the mysteries of the primes (the Riemann Hypothesis), the limits of computation (P=NP), and the puzzles of shapes in higher dimensions (the Poincare Conjecture). This talk will explain the Seven Millennium Problems and, in so doing, give a window into the world of mathematical research.